Status: Normative for the CFDL expression language (implemented by cfdl-calc, exposed through cfdl-expr).

CFDL expressions are bare, Excel-familiar formulas written directly in model source:

amount = base_rent * (1 + escalation) ^ (time.t / 12)
active when time.t >= 6

They are deterministic and terminating by construction: no loops, no recursion, no I/O, no user-defined functions. Every expression, on the same inputs, always produces the same value.

1. Numeric semantics

Two evaluation modes exist; models always run in decimal mode.

• Decimal mode (default). All arithmetic is exact 128-bit decimal (rust_decimal, 28 significant digits). 0.1 + 0.2 == 0.3 is true. Float64 is used ONLY as a documented escape for transcendental operations: fractional exponents (x ^ 0.5), and iterative solvers (rate, cpr_to_smm). Integer exponents are decimal-exact.
• excel_compat mode. Available to benchmark harnesses via cfdl_expr::eval_with_mode. All arithmetic runs in IEEE-754 float64, reproducing Excel's representation artifacts (0.1 + 0.2 - 0.3 yields ~5.55e-17, exactly as Excel does). Used to prove parity against Excel reference models and to explain decimal-vs-float differences.

Rounding: round() follows Excel semantics (half away from zero), not banker's rounding. round_down/round_up truncate toward/away from zero.

2. Syntax

• Operators, by precedence (loosest to tightest): or < and < not < comparisons (==, !=, <, <=, >, >=) < + - < * / % < unary - < ^ (right-associative).
• = and <> are accepted as Excel-style aliases for == and != inside expressions.
• Literals: decimal numbers (1200, 0.05, 1_000_000), true/false, double-quoted strings.
• Variables are dotted paths resolved from the host environment (see §3).
• Function calls are lowercase snake_case: pmt(0.005, 360, 100000).

3. Namespaces

The host (compiler or engine) provides values under five roots:

Unknown variables are hard errors (EXPR_EVAL), not nulls.

4. Builtin functions

Conditionals & aggregates: if(cond, a, b) (lazy — only the taken branch is evaluated), min, max, sum, avg, abs.

Rounding: round(x, [digits]), round_down(x, [digits]), round_up(x, [digits]).

Math: pow(base, exp) (function form of ^), clamp(x, lo, hi).

Time value of money (Excel sign conventions, decimal-exact for whole-period terms). Excel sign conventions mean pmt returns a negative number for a positive pv — a loan payment is money leaving. On a stream already declared outflow, negate it (amount = -pmt(...)), or the two negatives cancel and the payment registers as income: pmt(rate, nper, pv, [fv], [due]), pv(rate, nper, pmt, [fv], [due]), fv(rate, nper, pmt, [pv], [due]), nper(rate, pmt, pv, [fv], [due]), rate(nper, pmt, pv, [fv], [due], [guess]) (Newton solver, f64, tolerance 1e-12), ipmt(rate, per, nper, pv, [fv]) / ppmt(rate, per, nper, pv, [fv]) (interest/principal split of payment per, 1-based; ordinary annuities).

Depreciation: macrs_rate(year, life) — IRS Pub 946 GDS half-year convention percentages for 5/7/15/20-year property (year is 0-based; 0 beyond the recovery period).

Credit: cpr_to_smm(cpr).

Curves: curve_value(name, date) looks up a model-declared curve statement at a date. step curves (the default) are flat-forward: the last point at or before the query date (the first value before the first point). linear curves interpolate linearly in calendar days between bracketing points and clamp flat outside the declared range. Referencing an undeclared curve is an evaluation error.

Cross-stream series (phase-2 streams): series_sum(name, from_t, to_t) / series_avg(name, from_t, to_t) aggregate another stream's signed per-period amounts over an inclusive period window (prefix.* wildcards supported). Streams calling these evaluate in a second phase against finished phase-1 series — phase-2 streams cannot reference each other, so cycles are impossible by construction. Windows may extend into the projection tail (time ... project <n>), which is computed for valuation lookups but excluded from cash results and NPV.

Dates: date(y, m, d), parse_date(text) (ISO YYYY-MM-DD or YYYY-MM), edate(d, months), eomonth(d, months), months_between(d1, d2), year_frac(d1, d2, basis). Date arithmetic: d2 - d1 yields days; d + n / d - n shift by days.

Day-count bases for year_frac: "30/360" (aliases "30/360 us", "bond"), "30e/360" (alias "eurobond"), "act/360", "act/365", per ISDA/SIFMA definitions.

Business days: is_business_day(d, calendar), roll(d, convention, calendar), add_business_days(d, n, calendar).

• Calendars: "weekend" / "none" (weekends only), "us" / "us_federal" / "sifma", "target" / "target2" / "eur", "uk" / "uk_bank" / "london".
• Roll conventions: "none", "following", "modified_following", "preceding", "modified_preceding".

roll(parse_date("2027-01-01"), "following", "us")   -- next US business day
add_business_days(time.date, 2, "london")           -- T+2 on the UK calendar

5. Errors and diagnostics

Every parse and evaluation error carries a byte-offset span into the expression source. The compiler surfaces them as diagnostics with code EXPR_PARSE; runtime failures surface as EXPR_EVAL warnings in Results (the engine substitutes 0 / false and records the warning).

6. IR representation

Expressions are stored in IR as their raw source text with "lang": "cfdl":

{ "lang": "cfdl", "src": "50000 * pow(1.15, time.t / 12.0)" }